An engine cooling device provided at an automotive engine or the like is an example of such a fluid cooling device. In a water-cooled engine, such as an automotive engine, water (cooling water) has been used as a medium (coolant) for cooling a cylinder or cylinder head. An engine cooling device is configured such that the cooling water is supplied into a water jacket, which is formed inside the cylinder block of the engine, and forcibly circulated to cool the engine. The supply of the cooling water is performed by a cooling water supply pump driven by the engine, and the engine is cooled by the cooling water which is supplied into the water jacket in an amount corresponding to the revolution speed of the engine (see, for example, Patent Document 1). The cooling water supply pump is required to have a capacity (pump capacity) to supply cooling water such as to prevent the engine from overheating even under severe operation conditions under which the engine load is large. Thus, the cooling water supply pump is required to have a large pump capacity that makes it possible to prevent the engine from overheating when used in combination with a radiator even under assumed severe operation conditions, rather than the capacity required under normal operation conditions.